Saturday, April 18, 2009

Complex Numbers

The complex numbers are the combination of the real numbers with the imaginary numbers. They are written as the real part plus the imaginary part. For example:

2 + 3i

The imaginary number i is defined as the square root of minus one, so i2 = -1. Multiplication of complex numbers follows the same rules as the real numbers, you just have to keep track of each part of the multiplication:

We can add, subtract, multiply and divide any two complex numbers and get a complex number* back (except dividing by zero). And, unlike the real numbers, we can raise any complex number to any other complex number without restriction.

* the complex numbers include all real numbers. So 2 is the complex number 2 + 0i. Even though some complex multiplications give answers that are part of the real numbers, those answers are still complex numbers. For example (2 +3i) × (2 - 3i) = 13 (a real number) = 13 + 0i (a complex number).